论文标题
从轨道理论的角度来看，谐波振荡器相干状态
Harmonic oscillator coherent states from the orbit theory standpoint
论文作者
论文摘要
我们从原始开发的线性偏微分方程的非共同集成方法的角度研究了量子谐波振荡器的已知相干状态。该方法的应用是基于schrödinger方程的对称属性以及Lie组的共同连接表示的轨道几何形状。我们已经表明，通过非交通整合构建的相干状态的类似物可以根据振荡性谎言层代数的谎言组的微分方程系统的解决方案来表达。构建的解决方案与Hilbert空间在拉格朗日submanifold上与Coadhechaint代表轨道上的Hilbert空间功能上的Lie代数的不可还原表示直接相关。
We study the known coherent states of a quantum harmonic oscillator from the standpoint of the original developed noncommutative integration method for linear partial differential equations. The application of the method is based on the symmetry properties of the Schrödinger equation and on the orbit geometry of the coadjoint representation of Lie groups. We have shown that analogs of coherent states constructed by the noncommutative integration can be expressed in terms of the solution of a system of differential equations on the Lie group of the oscillatory Lie algebra. The solutions constructed are directly related to irreducible representation of the Lie algebra on the Hilbert space functions on the Lagrangian submanifold to the orbit of the coadjoint representation.
